The Research On The Time-dependent Koiter Model And Its Algorithm

Elastic shells are applied in the fields of aerospace, civil construction, petroleum and petrochemical, nuclear industry and many other engineering. Because of its wide applications,the theory of elasticity is one of the most important branches of the theory of elastic shells.Many scholars focused on the research of elastic shells, and proposed several mathematical models. The most classic and widely recognized model is the Koiter model. Under specific geometric assumptions, spatial assumptions and various boundary conditions, Ciarlet and his colleagues classified the shell into membrane shell, flexural shell, and so on. In this paper,based on the theory of elastostatics and elastodynamics, combined with the knowledge of differential geometry, tensor analysis, finite element and finite difference, we discuss the time-dependent Koiter shell, the time-dependent generalized membrane shell model and the time-dependent flexural shell model. According to the available literatures, it is the first time to give the numerical solutions to these elastodynamics models. This thesis mainly includes three aspects as follows:(1)The existence and uniqueness of the solution of the time-dependent Koiter model are proved. We semi-discretize the space variable with finite element method and fully discretize the problem using the time discretization by the Newmark scheme. The corresponding analyses of existence, uniqueness, stability, convergence and a priori error estimate are given. Finally,the numerical experiment of the special spherical shell is demonstrated to verify the stability and efficiency of the model.(2)We present the existence and uniqueness of the solution of the time-dependent generalized membrane shell model. The finite element method is used to semi-discretize the spatial variables and the fully discretized method using time discretization by the Newmark scheme is taken. We prove the existence and uniqueness of solutions of discrete solutions and the stability analysis and a priori error estimation of the proposed scheme. Finally, numerical experiments are done on special hyperbolic shells and conical shells to verify the stability and efficiency of the model.(3) We show that the solution of the time-dependent flexural shell model exists and is unique.We semi-discretize the space variable with finite element method and fully discretize the problem using the time discretization by the Newmark scheme. The corresponding analyses of existence, uniqueness, stability, convergence and a priori error estimate are given. Finally, the numerical experiments of special cylindrical shells and conical shells are carried out to verify the stability and efficiency of the model.